Halftone screens

Abstract

A method comprises forming a halftone screen set comprising first, second and third halftone screens. A first regular halftone screen for the screen set is selected. A second regular halftone screen is determined, using a processor, by performing a regularity invariant transformation on the first regular halftone screen. A third halftone screen is determined based on at least one predetermined condition being satisfied between the first, second and third halftone screens.

What is claimed is: 
     
         1 . A method comprising:
 selecting a first regular halftone screen;   determining a second regular halftone screen, using a processor, by performing a regularity invariant transformation on the first regular halftone screen; and   determining a third halftone screen to form a halftone screen set comprising the first screen, the second screen and the third screen, wherein the third halftone screen is determined based on at least one predetermined condition being satisfied between the first, second and third halftone screens.   
     
     
         2 . The method according to  claim 1  wherein the regularity invariant transformation performed on the first regular halftone screen to determine the second regular halftone screen is a rotation by an angle of 90 degrees minus twice the screen angle of the first regular halftone screen. 
     
     
         3 . The method according to  claim 1  wherein selecting the first halftone screen comprises iterating over a plurality of screens until a screen is found having a regularity index equal to 1 and having a number of lines per inch within a predetermined range. 
     
     
         4 . The method according to  claim 1  wherein the third halftone screen is determined based on a condition that each of a plurality of moiré frequencies between the first, second and third halftone screens is above a predetermined threshold. 
     
     
         5 . A method according to  claim 1  wherein the third halftone screen is determined based on a computed regularity index of the third halftone screen being less than or equal to a predetermined threshold. 
     
     
         6 . A method according to  claim 1  wherein the third halftone screen is determined based on a computed rosette size formed by the first screen, the second screen and the third screen having a diameter less than or equal to a predetermined threshold. 
     
     
         7 . A non-transitory computer-readable medium comprising instructions that, when executed by a processor, cause the processor to:
 generate a plurality of halftone images using a halftone screen set comprising a first halftone screen, a second halftone screen and a third halftone screen;   wherein each of a first screen and a second screen of the halftone screen set includes a vertical distance and a horizontal distance between neighboring halftone cell centers, the vertical and horizontal distances each equal to a first integer multiple of a dot pitch, and   the first screen is a regular screen and is related to the second screen by a transformation which maintains regularity when performed on a regular screen;   and wherein the third screen is such that a predetermined condition between the first screen, the second screen and the third screen is satisfied.   
     
     
         8 . A computer-readable medium according to  claim 7  wherein the second screen is related to the first screen by a rotational transformation by an angle of 90 degrees minus two times the screen angle of the first screen. 
     
     
         9 . A computer-readable medium according to  claim 7  wherein the halftone screen set forms moiré frequency vectors for each of a plurality of moiré orders having a minimum frequency at or equal to a predetermined threshold frequency, wherein a moiré frequency vector is a linear combination of fundamental frequency vectors of each the halftone screens which the halftone screen set comprises multiplied by integer coefficients, wherein a moiré order is a sum of absolute values of the integer coefficients, and wherein a fundamental frequency vector includes a first component proportional to an inverse of a cell size multiplied by a cosine of a screen angle relative to a dot grid and a second component proportional to the inverse of the cell size multiplied by a sine of the screen angle. 
     
     
         10 . A computer-readable medium according to  claim 7  wherein the third halftone screen has a regularity index less than or equal to a predetermined threshold. 
     
     
         11 . A computer-readable medium according to  claim 7  wherein the halftone screen set has a rosette having a diameter less than or equal to 0.24 mm. 
     
     
         12 . A computer-readable medium according to  claim 7  wherein:
 the dot grid has a number of dots per inch of 1625.6; 
 the first screen has an angle of approximately 15.9 degrees and a number of lines per inch of approximately 223.29; 
 the second screen has an angle of approximately 74.1 degrees and a number of lines per inch of approximately 223.29; and 
 the third screen has an angle of approximately 45 degrees and a number of lines per inch of approximately 216.88. 
 
     
     
         13 . A system, comprising:
 a color engine to separate an image into a plurality of color components; and   a halftone engine to generate a plurality of halftone images based on the plurality of color components and a plurality of halftone screens; wherein   the plurality of halftone screens comprises a first halftone screen, a second halftone screen and a third halftone screen; and wherein
 each of the first halftone screen and the second halftone screen has a regularity index equal to 1, wherein the regularity index of a screen is a least common multiple of denominators of components of a basis vector of the screen, and wherein a first component of the basis vector is calculated based on a cell size multiplied by a cosine of a screen angle relative to a dot grid, and a second component of the basis vector is calculated based on the cell size multiplied by a sine of the screen angle; 
 the first halftone screen and the second halftone screen are related by a regularity invariant transformation; and 
 the third halftone screen satisfies a predetermined condition between the first, second and third halftone screens. 
   
     
     
         14 . The system according to  claim 13  wherein the regularity invariant transformation is a rotation by an angle of 90 degrees minus two times the screen angle of the first screen. 
     
     
         15 . The system according to  claim 13  wherein the plurality of halftone screens forms a high frequency moiré pattern when the halftone screens are overlaid on each other. 
     
     
         16 . The system according to  claim 13  wherein the third halftone screen of the halftone screen set has a regularity index less than or equal to a predetermined threshold. 
     
     
         17 . The system according to  claim 13  wherein the halftone screen set produces a rosette having a diameter less than or equal to a predetermined threshold. 
     
     
         18 . The system according to  claim 13  wherein the first screen is a cyan screen, the second screen is a magenta screen and the third screen is a black screen.